When I was job-hunting out of college I had a personal website. I thought it was a great tool and a great place to showcase my work.
Now that I'm on the other side of the coin and working very closely with recruiting and hiring, I'm not sure how useful a personal website is for a stage manager who's job hunting. For designers it's a great place to showcase some photos and for a potential employer to get a feel for their work. As a stage manager though, there's nothing on your website you can't put on your resume.
Some will argue that it's nice to have a "professional" looking email address, but again, being on the other side of the coin I really don't think less of a potential employee for having a gmail, hotmail, yahoo, etc... as long as it's an email address that makes good business sense that's in front of the @. I got an application a few days ago from an email address to the tune of "jesus freak" and some numbers @ something.com... not terribly attractive to someone looking for a stage manager.
All in all I think it can be a nice touch to have a personal website, though it's certainly not necessary and in my opinion doesn't give you an edge in getting a stage management job.